Franziska Hinkelmann

Hinkelmann Picture    Graduate Research Assistant
   Ph.D. Candidate
   Virginia Bioinformatics Institute
   Washington Street, MC 0477
   Virginia Tech, Blacksburg, VA 24061
   fhinkel@vt.edu

   Curriculum Vitae
   Ph.D. Advisor Reinhard Laubenbacher


My research interest is in dynamic models in systems biology, with an emphasis on discrete models. My research includes model inference, analysis, and optimal control. I use polynomial dynamical systems as the mathematical framework for discrete models. This provides access to methods from algebraic geometry and computer algebra for model analysis. I am currently working on optimal control and bifurcation analysis for discrete models applied to problems in cancer systems biology.

Career Statement

Although a young researcher, my career goal would be to become an academic professor at an internationally renowned research institution performing cutting-edge applied mathematics pursuant to tomorrow's problems. Together with a team of researchers and interdisciplinary collaborators we would advance the area of applied mathematics by aiming to develop and apply new theorems to solve mathematical problems that have been inspired by real life biological problems.

Publications

Publication List
  • ADAM: Analysis of Discrete Models of Biological Systems Using Computer Algebra Franziska Hinkelmann, Madison Brandon, Bonny Guang, Rustin McNeill, Greg Blekherman, Alan Veliz-Cuba, Reinhard Laubenbacher, BMC Bioinformatics, DOI: 10.1186/1471-2105-12-295
  • Fast Groebner Basis Computation for Boolean Polynomials, Franziska Hinkelmann, Elizabeth Arnold, 2010, under review, arXiv:1010.2669
  • Mathematical Framework for Agent Based Models of Complex Biological Networks, Franziska Hinkelmann, David Murrugarra, Abdul S. Jarrah, Reinhard Laubenbacher, Bulletin of Mathematical Biology, 2010,
    DOI: 10.1007/s11538-010-9582-8
  • Inferring Biologically Relevant Models: Nested Canalyzing Functions, Franziska Hinkelmann, Abdul S. Jarrah, under review, arXiv:1011.6064
  • Parameter estimation for Boolean models of biological networks, Elena Dimitrova, Luis David Garcia-Puente, Franziska Hinkelmann, Abdul S. Jarrah, Reinhard Laubenbacher, Brandilyn Stigler, Michael Stillman, Paola Vera-Licona, Journal of Theoretical Computer Science, 2010, DOI: 10.1016/j.tcs.2010.04.034
  • Boolean Models of Bistable Biological Systems, Franziska Hinkelmann, Reinhard Laubenbacher, Journal of Discrete and Continuous Dynamical Systems - Series S (DCDS-S), 2010, DOI: 10.3934/dcdss.2011.4.1443
Ph.D. Dissertation

Upcoming Talks

  • Plenary Talk, MBI (Mathematical Biosciences Institute), Workshop: Algebraic Methods in Evolutionary and Systems Biology, May 2012, Columbus, OH
  • SACNAS conference, October, 2011, San Jose, CA
  • Georgia Tech, Mathematical Biology Seminar, September 21, 2011, Atlanta, GA
  • MBI Postdoc Seminar, Algebraic theory for discrete models in systems biology, September 8, 2011; 10:30-11:30am, Jennings Hall, OSU, Columbus, OH

Research

Mathematical modeling is a very powerful tool for analyzing and understanding a biological system. For systems discrete in nature, like many biological systems, algebraic modeling techniques are suitable. Unlike continuous systems, which have a wide range of theorems and software available for model generation (e.g., parameter estimation) and simulation (e.g., solving differential equations), very few tools exist for discrete networks.

My goal is to find practical methods to analyze the dynamics of discrete models using abstract algebra instead of exhaustive enumeration, which is often infeasible due to model size, or simulation, which only explores a fraction of possible configurations.

Wnt Signaling in Melanoma

Alterations in Wnt signaling are not thought to be causative for melanoma, however activation of signaling in this pathway is common. This occurs in the absence of the mutations in pathway proteins often noted in tumors such as colon cancer. The hallmark of activated Wnt signaling is nuclear localization of beta-catenin, which is then capable of enhancing transcription of genes including Cyclin D and c-Myc.

In collaboration with Dr. Delidow at Marshall University, we are currently working on a discrete model of this pathway.

Optimal Control for Agent-Based Models

An agent-based model of a complex system consists of agents and rules that describe how they interact. A well known example is the agent-based model for the spread of an infectious disease by social interaction among agents (humans). We recently published an algorithm for approximating an agent-based model with an algebraic model.

My current research focuses on developing control theory within this framework. I am using an agent-based model of cytokine-directed clinical trials and am developing optimal control strategies for possible treatments of systemic inflammatory response syndrome (SIRS)/multiple organ failure (MOF).

Dynamics of Discrete Models

Most discrete models can be expressed as algebraic models. This includes Logical models, Petri-nets, Agents-based models, and Probabilistic Boolean networks. During a summer Research Experience for Undergraduates (REU) 2010, my students developed software to translate a Logical model into an Algebraic model and to analyze its dynamics.

Algebraic Statistics

I am interested in coordinating efforts between Algebraic Statistics and Macaulay2, a computer algebra system. Here are some slides from algebraic statistics lectures I have given.

Mentoring

I have mentored several undergraduate students in exciting research projects.

  • Mentor Research Experiences for Undergraduates (REU), Modeling and Simulation in Systems Biology (MSSB), Summer 2011
    • Mentoring a group of four undergraduates during a 10 week project
    • Two papers in preparation: Optimal Control for Polynomial Dynamical Systems and Converting Complex Agent-based Models into Polynomial Dynamical Systems
  • Mentor for Undergraduate Research, Mathematical Modeling for Biologists, Knockout and Knock- down, Spring 2011
    Mentoring an individual student in his undergraduate research
  • Mentor for Undergraduate Research, Database for Discrete Models of Biological Models, Fall 2010
    Mentoring an individual student in his undergraduate research
  • Mentor Research Experiences for Undergraduates (REU), Modeling and Simulation in Systems Biology (MSSB), Summer 2010
  • Mentor for Initiative for Maximizing Student Development (IMSD) Undergraduate Research, Network Modeling, Spring and Summer 2009
    Mentoring an individual student in his undergraduate research
  • Mentor for Undergraduate Research, Network Modeling, Fall 2008
    Mentoring an individual student in her undergraduate research

Software

Teaching

If you would like to use my slides or other material (exams, quizzes, 3D animations), feel free to send me an email and I would be happy to share them with you.